WASHINGTON — Not wasting any time, new Senate Majority Leader Mitch McConnell and President Barack Obama are setting course for showdowns over health care, a big oil pipeline, immigration policy and financing of the agency that tries to protect the U.S. from terrorists.

At the same time, both insist they are eager for compromise — if only the other side would give in.

"It seems with every new day, we have a new veto threat from the president," McConnell, R-Ky., complained Wednesday, his second day as Senate leader. Republicans won control of the chamber in the November elections, and strengthened their hold on the House.

With the 114th Congress just getting underway, the White House already has announced that Obama stands ready to veto three bills that Republicans hope to rush through. One would allow construction of the Keystone XL pipeline to bring oil from Canada. Another weakens Obama's signature health care law, by increasing the definition of a full-time employee who must be offered health coverage at work to 40 hours from the current 30. The third would alter a key provision of the 2010 Dodd-Frank overhaul of financial services regulations.

"The president is not going to set the agenda for us here in the Senate," McConnell told reporters.

Lamenting the deadly attack on a satirical newspaper in Paris, McConnell said the attack underscores that the war on terrorism is not over. He declined to say whether the attack would affect Republican plans to use the Homeland Security Department's budget as leverage against Obama's immigration policy.

"But at the end of the day, we're going to fund the department, obviously," McConnell said.

The anti-terrorism agency's budget expires in late February, and Republicans have been working on a plan to tie new funding to a measure overturning Obama's action that eased immigration rules last year and decreased deportations. McConnell said "we'll decide in February how to handle it."

Tea party-backed Sen. Ted Cruz, one of the loudest voices against Obama's immigration policy, said there was no reason to pull back from stopping the president's "abuse of power and his unconstitutional actions."

It's Obama who should worry about the security risks if he considers a veto that would shut down the Homeland Security Department, said Cruz, R-Texas.

Even as McConnell and Obama skirmished from afar, both maintained there is hope for bipartisan cooperation.

Obama, who meets with Republican congressional leaders next week, said he expects "some pitched political battles" but is hopeful for a "productive 2015."

In his first big speech as majority leader, McConnell talked of working with Obama on trade agreements, infrastructure improvements and rewriting tax laws.

He even raised the prospect of tackling some big issues that have bedeviled Congress for years, such as shoring up Medicare and Social Security, balancing the budget and whittling away the national debt.

"But bipartisan reform can only be achieved if President Obama is interested in it," McConnell said. "The president is the only one who can bring his party on board."